Like any computer algebra system, it applies a number of rules to simplify the function and calculate the derivatives according to the commonly known differentiation rules. Maxima takes care of actually computing the derivative of the mathematical function. This time, the function gets transformed into a form that can be understood by the computer algebra system Maxima. When the "Go!" button is clicked, the Derivative Calculator sends the mathematical function and the settings (differentiation variable and order) to the server, where it is analyzed again. MathJax takes care of displaying it in the browser. This allows for quick feedback while typing by transforming the tree into LaTeX code. The parser is implemented in JavaScript, based on the Shunting-yard algorithm, and can run directly in the browser. The Derivative Calculator has to detect these cases and insert the multiplication sign. A specialty in mathematical expressions is that the multiplication sign can be left out sometimes, for example we write "5x" instead of "5*x". In doing this, the Derivative Calculator has to respect the order of operations. It transforms it into a form that is better understandable by a computer, namely a tree (see figure below). ![]() Just enter you own examples above and they will be calculated immediately step-by-step.For those with a technical background, the following section explains how the Derivative Calculator works.įirst, a parser analyzes the mathematical function. To find the equation of the function, you have to insert a point and get an equation which gives the y-axis intercept. To calculate the slope m, use the formulaĪs we can see, the slope was calculated first. This means: You calculate the difference of the y-coordinates and divide it by the difference of the x-coordinates. How to calculate the equation of a linear function from two given points?įirst, we have to calculate the slope m by inserting the x- and y- coordinates of the points into the formula. Therefore, the equation of the function is General form of the linear function: f(x)=mx+b Here is an example: Lets assume we know that our function has slope and goes through (-2|5).Ĭalculate the y-axis intercept b by inserting: the one coordinate for x and the other one for f(x). You have to insert the point into the equation, i.e. How to calculate the equation of the line from a point and the slope? If you take a look on the function graphs, you see that intersects the y-axis at intersects the y-axis at. As the name says, it says where the function cuts the y-axis. The y-line intercept is the number at the end of the function. What is the y-line intercept of a linear function? This means whenever we go one square to the right, we have to go three squares down to be on the graph again. ![]() If we go one square to the right of any point on the graph, we have to go two squares up to be on the graph again.Īnother example, this time with negative slope: It says how may units you have to go up / down if you go one unit to the right. The slope of a linear function corresponds to the number in front of the x. ![]() The graph of a linear function is always a line.Ī similar word to linear function is linear correlation. Here is an example:ĭein Browser unterstützt den HTML-Canvas-Tag nicht. The general form of a linear function is, where m is the slope and b is the y-axis intercept. A linear function is a function whose graph is a line.
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